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## New Year party

Posted by Chris on January 27, 2012 – 2:25 pm

Here’s an oldie. I think it’s an excellent logic puzzle.

My wife and I invited four other couples to our New Year’s Eve bash. After yelling “Happy New Year!”, everyone either shook hands with or hugged each other. The couples only hugged each other.

When I asked everyone how many people they shook hands with, each gave a different answer.

How many people did my wife shake hands with?

How many people did I shake hands with?

This post is under “Logic” and has 12 respond so far.

### 12 Responds so far- Add one»

1. 1. ragknot Said：

Four other couples should have made a total of ten people.
If everyone shook hands with everyone else that would make 9 hand shakes for everyone, but you said couples hugged each other , so if they didn’t shake hands with their couple that would be eight handshakes for each person.

Did anyone shake their own hand?
What is it I missed?

2. 2. ragknot Said：

Copied…Pasted.

Eketahuna said…

The straggler knew 2 people at the party.
MARCH 17, 2010 6:07 PM

That was cool. Did a stranger arrive at your New Year’s Bash?

3. 3. Fireball Said：

if it said each couple hugged each other that means 5 people hugged and eight handshakes for each person not 9 because couples hug not handshake. also i have a question, did it mean that “my wife and i” each invited four couples separately or together?

4. 4. Curtis Said：

Both you and your wife shook hands with four guests each.

5. 5. Curtis Said：

The important clue is that each guest gives a different answer.

As already noted, after hugging their spouse, each guest has to greet 8 other people.

Thus the answers they give have to be 1 thu’ 8.

By putting the greetings on a 10 x 10 grid the answer is revealed.

Sadly my computer skill falls short of posting the completed grid.

6. 6. Chris Said：

Hi Curtis, you got it. Post your grid – I’ll straighten it up.

Hi Ragknot, you looked up the wrong past question.

7. 7. Curtis Said：
```      M    W   A1   A2   B1   B2   C1   C2   D1   D2
M     x    h    h    h    h    h    s    s    s    s
W     h    x    h    h    h    h    s    s    s    s
A1    h    h    x    h    h    h    h    h    h    s
A2    h    h    h    x    h    h    h    h    s    s
B1    h    h    h    h    x    h    h    s    s    s
B2    h    h    h    h    h    x    s    s    s    s
C1    s    s    h    h    h    s    x    h    s    s
C2    s    s    h    h    s    s    h    x    s    s
D1    s    s    h    s    s    s    s    s    x    h
D2    s    s    s    s    s    s    s    s    h    x
```

M= man, W= wife, A1+ A2= couple A etc
x = you don’t greet yourself!, h = hug, s = shake
Having filled in the X’s and the compulsory hugs, one guest has to shake everyone’s hand (D2),
Therefore one guest can shake with no one else except D2 (A1)
And so you continue with, 7 and 2, 6 and 3, etc. until grid is complete.

Regards, Curtis

8. 8. Chris Said：

Copy/paste/edit …
There were 10 people altogether. So the most handshakes that any of them could have made is 8 (you don’t shake hand with yourself or your partner). As each of the nine people gave a different answer, the answers must have been 0,1,2,3,4,5,6,7,8.

I’ll identify the people by the number of hands that they shook, and I’ll use M to identify myself. The obvious bit is that 8 must have shook with everyone except himself and his partner. So those eight people must have shook at least once. So 0 must be 8’s partner. 7 can’t have shook hands with 0 (as nobody shook 0’s hand), neither can 7 shake hands with 1 as 1’s handshake was with 8. 7 must have shook hands with everyone except 0 and 1, so 1 must be 7’s partner. Similarly, 6’s partner is 2 and 5’s partner is 3.

8 shook hands with 7,6,5,4,3,2,1,M and is coupled with 0.
7 shook hands with 8,6,5,4,3,2,M and is coupled with 1.
6 shook hands with 8,7,5,4,3,M and is coupled with 2.
5 shook hands with 8,7,6,4,M and is coupled with 3.
4 shook hands with 8,7,6,5 (see above) and is coupled with M(e).
3 shook hands with 8,7,6 and is coupled with 5.
2 shook hands with 8,7 and is coupled with 6.
1 shook hands with 8 and is coupled with 7.
0 shook hands with nobody and is coupled with 8.
M shook hands with 8,7,6,5 and my wife is 4
So my both my wife and I shook hands 4 times. We both shook hands with the same people.

9. 9. Bekki Said：

@Chris
0 must have either been rude or didn’t follow the instructions to have not shaken anyone’s hand. “After yelling “Happy New Year!”, everyone either shook hands with or hugged each other. The couples only hugged each other.”

Unless there are instructions that are missing, or I’m misunderstanding.

10. 10. Chris Said：

Hi Bekki, 0 hugged everyone.

11. 11. Bekki Said：

I guess it’s the misunderstsanding part. “The couples only hugged each other” got mis-read as “only the couples hugged each other.”

12. 12. Lordish Said：

Redo you math : men shake hands to men, and hug women
Women hug everyone
Therefore :
Husband : shook 4 hands
Women : shook 0 hands =)

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